If you do not close a file, you will run out of resources for more files. In Linux the default is 1024 open files per process, this is because a "file handle" is an index into a table (i.e. indexing an array). How it's handled on Windows I don't know, but sooner or later the process is going to run out of resource if you just keep on opening files but not closing them.
On the other hand, if you open a single file, that you use throughout the lifetime of the program, then there is no need to open/close it all the time. Open it once and leave it open. Also, all open files will be closed when exiting the process, so if your program just does some quick processing of a file and then exiting you don't have to close it. However, if I was reviewing the code I would still add a note about it, if you allocate a resource (memory, files, something else) I think you should release it when done with it even if it's done automatically by the system.